EXAM-(M) 2018 MECHANICAL ENGINEERING

Paper -II

FSI-D-MCHE

Time Allowed: Three Hours Maximum Marks : 200

Question Paper Specific Instructions

Please read each of the following instructions carefully before attempting questions:

There are EIGHT questions in all, out of which FIVE are to be attempted.

Questions no. 1 and 5 are compulsory. Out of the remaining SIX questions, THREE are to be attempted selecting at least ONE question from each of the two Sections A and B.

Attempts of questions shall be counted in sequential order. Unless struck off attempt of a question shall be counted even if attempted partly. Any page or portion of the page left blank in the Question-cum-Answer Booklet must be clearly struck off.

All questions carry equal marks. The number of marks carried by a question/pan is indicated against it.

Answers must be written in ENGLISH only.

Unless otherwise mentioned, symbols and notations have their usual standard meanings.

Assume suitable data, if necessary and indicate the same clearly.

Neat sketches may be drawn, wherever required.

Newton may be converted to kgf using the equality 1 kilonewton (1 kN) ---- 100 kgf, if found necessary.

All answers should be in SI units.

Take: 1 kcal = 4.187 kJ and 1 kg I cm2 — 0.98 bar

1 bar = 105 pascals

Universal gas constant = 8314.6 JIkmol-K

Psychrometric chart is enclosed.

FSI- D- MCHE

SECTION A

Ql. (a) Derive a general expression for the change in entropy of a real gas obeying the van der Waals equation.

The boiling point of water at the top of a hill is found to be 90°C, whereas it boils at 99.6°C with the latent heat of evaporation of 2256-94 kJ/kg at the foot of the hill (where the pressure is 101.325 kPa). Assuming that the atmosphere is locally isothermal at 300 K (i.e. pv = povo is valid), estimate the height of the hill.

A house, that is losing heat at a rate of 50,000 kJ/h when the outside temperature drops to 4°C, is to be heated by electric resistance heaters. If the house is to be maintained at 25°C at all times, determine the reversible work input for this process and the irreversibility.

Determine the heat transfer rate from a rectangular fin of length 20 cm, width 40 cm and thickness 2 cm. The tip of the fin is not insulated and the fin has a thermal conductivity of 150 W/mK. The base temperature is 100°C and the fluid is at 20°C. The heat transfer coefficient between the fin and the fluid is 30 W/m2K.

What purposes does an expansion device serve in a vapour compression refrigeration system ? Explain how a simple capillary tube can serve these purposes.

8

8

8

8

8

Q2. (a) Prove that:

(aPjs _ k k (5P),

where k C C p v•

[Hint : C p_c

v al`)13

ravI2 rap)

Three thin walled infinitely long hollow cylinders of radii 5 cm, 10 cm

and 15 cm are arranged coaxially. The temperatures of the innermost

and outermost cylinders are respectively 1000 K and 300 K. Calculate

the steady state temperature of the middle cylinder surface and the heat flow per m2 area of the innermost cylinder. Assume emissivity of all the

cylinders to be 0.5 and vacuum in the spaces between the cylinders.

Take cy = 5.67 x 10-8 whn2K4. 15

Explain, with the help of T-s diagram, that for atmospheric moist air

Tdry bulb > Twet bulb > Tdew point, in unsaturated condition, and

Tdry bulb = Twet bulb = Tdew point, in saturated condition. 10

FSI- D- MCHE 2

15

Q3. (a) A refrigeration plant operates on Reversed Carnot cycle. The saturation temperatures in the condenser and evaporator are 40°C and — 5°C respectively. The volumetric efficiencies of the compressor and expander are 100 percent each.

Calculate (i) the refrigeration effect per kg of refrigerant, (ii) the coefficient of performance, (iii) the compressor displacement per kW of refrigeration effect, and (iv) the net work input per kg of refrigerant.

Also, calculate the corresponding for a simple vapour compression refrigeration cycle. Assume no superheating either at the inlet or exit of the compressor, and no subcooling.

Show the cycles on T-s diagram.

Explain, why in practice a throttle valve is used in vapour compression refrigeration rather than an expander cylinder.

The properties of the refrigerant are as follows .

(The specific volume of the saturated liquid is negligible compared to vapour).

Saturation Temperature

°C

Saturation Pressure

bar

Enthalpy, kJ/kg Entropy, kJ/kg K Specific Volume (m3/kg)

vg

h f h

g s f s g

40 9.6065 238.535 36715 11298 1.5405 1817

(-5) 2.6096 195-395 349-32 0.9831 1-5571 64-963

f and g refer to saturated liquid and saturated vapour respectively. 15

(b) A piston-cylinder device contains 0-8 kg of steam at 300°C and 1 MPa. Steam is cooled at constant pressure until one-half of the mass condenses. 15

Show the process on a T — V diagram. Find the final temperature. Determine the volume change. Determine the heat transfer.

Given:

Tables

P Tsat

v f

v g

hf

h g

(kPa) (°C) (m3/kg) (m3/kg) (kJ/kg) (kJ/kg)

1.000 6-97 0.00100 129.19 29-303 2513-7

100-0 99.61 0.00104 F6941 417.51 2675.0

1000.0 179.88 ft 001127 0-19436 762.51 27771

FSI- D- MCHE

3

Property:

At P = 1.00 MPa and T = 300°C

= 74246 kJ/kg-K

= 0-25799 m3/kg

h 3051.6 kJ/kg

(c) Water at 20°C flowing at the rate of 0.015 kg/s enters a 25 mm inner

diameter tube which is maintained at a temperature of 90°C. Assuming

hydrodynamically and thermally fully developed flow, determine the

heat transfer coefficient and the tube length required to heat the

water to 70°C.

Given water properties at 20°C; p = 1000.5 kg/m3, Cp = 4181-8 J/kg K,

Kinematic viscosity = F006 x 10-6 m2/s.

Properties of water at 45°C :

p = 992 kg/m3, Cp = 4180 J/kg K, k = 0.638 W/mK,

Kinematic viscosity = 0.613 x 10-6 m2/s.

The average Nusselt number for the tube is 3.657. 10

Q4. (a) In a parallel flow heat exchanger, engine oil enters a heat exchanger at

150°C and leaves at 80°C. The cooling water enters at 30°C and leaves

at 65°C. If the fluid flow rates and the inlet conditions are unchanged,

find exit temperature of each stream in counterflow exchanger. 15

(b) A building has the following calculated cooling loads :

RSH gain = 310 kW, RLH gain = 100 kW.

The building's inside space is maintained at the following conditions of

Room DBT = 25°C and Room RH = 50%. The outdoor air is at 28°C DBT

and 50% RH. And 10% by mass of air supplied to the building is outdoor

air. If the air supplied to the space is not to be at a temperature lower than 18°C, find

minimum amount of air supplied to the space in m3/s,

volume flow rate of air entering the coil,

capacity of the cooling coil in TR, and

ADP and bypass factor of the cooling coil.

Also, draw the layout sketch.

(Psychrometric chart is attached) 15

FSI- D- MCHE 4

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(c) In the early development of steam power plants, approximately 112 kg

of coal is required per kilowatt hour. Assume that the mean temperature at which heat was supplied is 175°C and heat was rejected is 100°C at

that time. Presently, assume that heat is supplied at a mean temperature of 380°C and rejected at 32°C. The ratio of the actual

thermal efficiency to that of the Carnot cycle today is about 1.25 times that of earlier years. Assuming the same heating value for coal in both

cases, calculate the amount of coal now required per kilowatt hour. 10

V

FSI- D- MCHE 6

SECTION B

Q5. (a) Compare the cooling effect of fuel evaporation on charge temperature in

a turbocharged spark ignition engine for the following two cases :

The carburettor is placed before the compressor

The carburettor is placed after the compressor

The specific heat capacity of the air and the latent heat of evaporation of

the fuel are both constant. For the air/fuel ratio of 12.5 : 1, the

evaporation of the fuel causes a 25 K drop in mixture temperature. The

compressor efficiency is 70% for the pressure ratio of 1-5, and the

ambient temperature is 15°C. Assume the following values :

for air, Cp = F01 kJ/kgK, y = 1-4,

for air/fuel mixture, Cp = F05 kJ/kgK, y = 1.34.

Finally, compare the compressor work in both cases. 8

A Ford 2-stroke engine has a swept volume of 1.2 litres. At a speed of

5500 rpm, the full load torque is 108 Nm and the brake specific fuel

consumption is 294 g/kWh. Calculate the brake mean effective pressure,

and the brake thermal efficiency (assume a calorific value of 43 MJ/kg).

Give at least 5 reasons why the brake thermal efficiency is lower than

the value predicted by the Otto cycles analysis. 8

What is meant by "work done factor" in the axial flow compressors ?

Explain how the work done factor value varies with the number of

stages. Why is the work done factor not considered in centrifugal

compressors ?

8

What is 'slip factor' for a centrifugal compressor stage ? What is its effect

on the flow and the pressure ratio in the stage? 8

FSI- D- MCHE 7

50 m

Generator

--> 5000 kg/s

Turbine

(e) Water in a large lake is to be used to generate electricity by the installation of a hydraulic turbine-generator located, where the depth of water is 50 m (see Figure). Water is to be supplied at the rate of 5000 kg/s. The electric power generated is 1862 kW and the generator efficiency is 95%. Determine (i) the overall efficiency of the turbine generator, (ii) the mechanical efficiency of the turbine, and (iii) the shaft power supplied by the turbine to the generator. -

Density of water is 1000 kg/m3 and gravitational acceleration is 9.81 m/s2.

Q6. (a) Reciprocating internal combustion engines have been fitted with ingenious mechanisms that allow the expansion ratio (re) to be greater than the compression ratio (re). When such a system is modelled by an ideal gas cycle there is

(i) heat addition at constant volume,

(U) some heat rejection at constant volume,

(iii) and some heat rejection at constant pressure, to complete the cycle.

The process is shown in the following figure on a T—s plane:

>

Depict the processes on a P-V plane. The constant-volume temperature

rise (2 3) is 0T1. Derive an expression for the cycle efficiency in terms

of re, re and 0. State any assumptions. 15

8 FSI- D- MCHE

In an ideal gas turbine cycle with reheat, air at state (P1, T1) is

compressed to (rpi). in the compressor and heated to T3x in the

combustion chamber. The air is then expanded in two stages, each

turbine having the same pressure ratio, with reheat to T3 between the

stages. Assuming the working fluid to be a perfect gas with constant

specific heats, and that the compression and expansion are isentropic,

show that the specific work output will be a maximum when 'r', the

compressor pressure ratio is given by

)2/3 r(Y— 1)/Y = ( 13

where y is the ratio of specific heats, Cp/c. Draw the schematic

arrangement of the cycle and the corresponding T—s diagram also. 15

C12H26 is burned at constant volume with no excess air. The initial temperature is 30°C. Assuming complete combustion, determine the theoretical maximum temperature when there is no dissociation. Use the following enthalpy values (J/mole) of different substances for the calculations :

10

C121-126 75, 79, 383

CO2 1, 46, 203

1120 1, 18, 329

N2 88, 122

Q7. (a) In a power plant employing Rankine cycle with reheat, superheated

steam at 150 bar and 500°C (h = 3310.6 kJ/kg; s = 6-3487 kJ/kg K)

enters the first stage of the turbine. The condenser is maintained at

0.1 bar (vf = 0-001 m3/kg, hf = 191-83 kJ/kg K, hg = 2584.8 kJ/kg,

sf = 0-6493 kJ/kg K, sg = 81511 kJ/kg K). The exit steam from the first

stage of turbine is reheated to 500°C before it is fed to the second stage

of the turbine. Calculate the thermal efficiency of the power plant if

steam expands to

90 bar in the first stage of the turbine.

60 bar in the first stage of the turbine. 15

FSI- D- MCHE 9

From the superheated steam tables at 90 bar

T (°C) h (kJ/kg) s (kJ/kg K)

400 3125.5 61067

500 3389.2 6.6728

From the superheated steam tables at 60 bar

T (°C) h (k.J/kg) s (kJ/kg K)

300 2885.0 6-0692

400 31801 6.5462

500 3422.2 6.8818

A gas engine operating on methane (CH4) at 1500 rpm, full throttle,

generates the following emissions measured on a dry volumetric basis :

CO2 10-4%

CO 11%

112 0.6%

02 0.9%

NO 600 ppm

HC 1100 ppm (as methane)

If the specific fuel consumption is 250 g/kWh, calculate the specific

emissions of carbon monooxide, nitrogen oxide, and unburned

hydrocarbons (that is g/kWh). Why is the specific basis more relevant

than a percentage basis?

15

A model of a torpedo is tested in a water filled towing tank at a velocity

of 244 m/s. The prototype is expected to attain a velocity of 6-1 m/s in

water. What would be the model speed if tested in a wind tunnel filled

with air at a pressure of 20.0 bar and constant temperature of 27°C ?

The absolute viscosity of air may be assumed as F845 x 10-5 N.s/m2, the

molecular weight of air as 28-97 kg/kmol and the universal gas constant

as 8115 kJ/kg-mol K. The kinematic viscosity of water may be taken as

113 x 10-6 m2/s. 10

FSI- D- MCHE 10

Q8. (a) Starting with the differential form of the conservation equations, show

that the flow velocity increases with heat addition in subsonic Rayleigh

flow, but decreases in supersonic Rayleigh flow Also, draw the

T-s diagram. 15

(b) At the mean diameter of a gas turbine stage, the blade velocity is

350 m/s. The blade angles at the inlet and exit are 200 and

54° (respectively) with respect to axial direction. The blades at this

section are designed to have a degree of reaction of 50 percent. The

mean diameter of the blades is 0.432 and the mean blade height is

0.07 m. Assuming that the whirl velocity varies inversely with respect to

radius, estimate:

the flow velocity,

the angles of blades at the tip and at the root, and

the degree of reaction at the tip and at the root of the blades. 15

(c) Briefly explain the stages of combustion in SI engines elaborating the

flame front propagation. 10

FSI- D- MCHE 11

I